Summary

Rate of Reaction: Defined as change in concentration per unit time:

$\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[B]}{dt}$ for $aA \rightarrow bB$.

Average rate over an interval; instantaneous rate from slope of tangent.

Rate Law & Order: $\text{Rate} = k[A]^m[B]^n$; $m+n$ = overall order (determined experimentally, not from stoichiometry).

$k$ = rate constant, units depend on order.

Integrated Rate Equations:

• Zero order: $[A] = [A]_0 - kt$; half-life $t_{1/2} = \frac{[A]_0}{2k}$.
• First order: $\ln[A] = \ln[A]_0 - kt$; $t_{1/2} = \frac{0.693}{k}$ (independent of initial concentration).
• Second order (single reactant): $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$; $t_{1/2} = \frac{1}{k[A]_0}$.

Pseudo-First Order: When one reactant is in large excess, order reduces to first (e.g., hydrolysis of ester in excess water).

Arrhenius Equation: $k = A e^{-E_a/RT}$;

$\ln k = \ln A - \frac{E_a}{R}\frac{1}{T}$.

$E_a$ = activation energy, $A$ = frequency factor.

Plot $\ln k$ vs $1/T$ gives straight line with slope $= -E_a/R$.

Effect of Temperature: Rate constant increases with $T$; a $10^\circ$C rise roughly doubles $k$ for many reactions.

Collision Theory: Molecules must collide with sufficient energy ($\geq E_a$) and proper orientation.

Fraction of effective collisions $= e^{-E_a/RT}$.

Molecularity: Number of molecules colliding in an elementary step (1, 2, or 3). Always a whole number; order may be fractional or zero. …